# Z-values and probability

#### chickennugget

##### New Member
Suppose concentration of arsenic (in ppb) in groundwater sampled quarterly from a particular well can be modeled with a normal distribution with a mean of 5 and a standard deviation of 1.

a) What is the probability that a single observation will be given greater than 7ppb?

$$z =5-7 / 1 = 2$$ And since we want greater than the probability would be 2.28.

http://imgur.com/r8jzeo4

What I'm confused on is the second part!
b)What is the probability that the average of four observations will be greater than 7 ppb?

So now, I have to take into account n, so the formula shifts from
$$z =Xi-7/ sd$$ to $$z =xbar-7 / [sd/sqrt(n)]$$

$$z =5-7 /[1/sqrt(4)]= -4$$ Therefore, the probability is 100?
Which doesn't make sense at all.

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